{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T17:45:45Z","timestamp":1649094345924},"reference-count":38,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> In this paper, one-generator binary quasi-cyclic (QC) codes are explored by statistical tools derived from design of experiments. A connection between a structured cyclic class of statistical designs, k-circulant supersaturated designs and QC codes is given. The mathematical structure of the later codes is explored and a link between complementary dual binary QC codes and E(s<jats:sup>2<\/jats:sup>)-optimal k-circulant supersaturated designs is established. Moreover, binary QC codes of rate 1\/3, 1\/4, 1\/5, 1\/6 and 1\/7 are found by utilizing a genetic algorithm. Our approach is based on a search for good or best codes that attain the current best-known lower bounds on the minimum distance of linear codes, formulated as a combinatorial optimization problem. Surveying previous results, it is shown, that our codes reach the current best-known lower bounds on the minimum distance of linear codes with the same parameters. <\/jats:p>","DOI":"10.1142\/s1793830911001127","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T13:20:39Z","timestamp":1310563239000},"page":"223-243","source":"Crossref","is-referenced-by-count":0,"title":["QUASI-CYCLIC CODES FROM CYCLIC-STRUCTURED DESIGNS WITH GOOD PROPERTIES"],"prefix":"10.1142","volume":"03","author":[{"given":"CHRISTOS","family":"KOUKOUVINOS","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece"}]},{"given":"DIMITRIS E.","family":"SIMOS","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-66-03307-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1978.1055930"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/18.971744"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1962.10490035"},{"key":"rf5","volume-title":"Handbook of Magma Functions","author":"Bosma W.","year":"2002"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/18.333888"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(69)90497-5"},{"key":"rf9","volume-title":"Handbook of Genetic Algorithms","author":"Davis L.","year":"1991"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/18.651076"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2009.01.002"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1126\/science.8346439"},{"key":"rf13","volume-title":"Genetic Algorithms in Search, Optimization, and Machine Learning","author":"Goldberg D. 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